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Divergence theorem

  1. May 15, 2009 #1
    1. The problem statement, all variables and given/known data

    use the divergence theorem to evaluate the integral F dot dA

    F = (2x-z)i + x2yj + xz2k

    s is the surface enclosing the unit cube and oriented outward

    2. Relevant equations



    3. The attempt at a solution

    is the the region from -1 to 1 for x y and z

    div F = x2 + 2xz + 2

    x2 + 2xz + 2 dx = x3/3 + x2z + 2x from -1 to 1

    14/3 dy = 14y/3 from -1 to 1 = 28/3

    28/3 dz = 28z/3 from -1 to 1 = 56/3

    is this correct
     
  2. jcsd
  3. May 15, 2009 #2

    HallsofIvy

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    Staff Emeritus
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    No, the "unit cube" is defined by [itex]0\le x\le 1[/itex], [itex]0\le y\le 1[/itex], [itex]0\le z\le 1[/itex].
     
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